Betti splitting via componentwise linear ideals.

A monomial ideal I admits a Betti splitting I = J + K if the Betti numbers of I can be determined in terms of the Betti numbers of the ideals J , K and J ∩ K . Given a monomial ideal I , we prove that I = J + K is a Betti splitting of I , provided J and K are componentwise linear, generalizing a result of Francisco, Hà and Van Tuyl. If I has a linear resolution, the converse also holds. We apply this result recursively to the Alexander dual of vertex-decomposable, shellable and constructible simplicial complexes. Moreover we determine the graded Betti numbers of the defining ideal of three general fat points in the projective space. [ABSTRACT FROM AUTHOR]